Bloomsburg University

Argumentation
James Tomlinson, Ph.D.

Statistics can be used as a powerful source in Argumentation.  But there are some real concerns about their use.  You should review the material presented here, and be prepared to follow these guidelines in class.

This is presented as a quick reference for you - I realize most of you have not had a stats course, but in Argumentation you need to have some basic understanding of statistics - to use in substantiating your position, or refuting an opponent's.

Terminology:

Correlation - this describes the direction and strength of a straight-line relationship between two variables.  Many people will make claims of a "correlation" (either positive or negative) without substantiation.  Why would this be?  Simply put, it is using the POWER of the word "CORRELATION" to imply this to be  factual - therefore indisputable - evidence!!!!!  If you argue a correlation exists, you have the ethical responsibility to DEMONSTRATE that relationship.  On the other hand, if someone is arguing a correlation, you also have a responsibility - make them demonstrate it - of course if they can, you could be in trouble !!!!
ALSO, remember - just because there is a "correlation" in the data, it does not mean there is a causal relationship.  To claim causation requires even more evidence !!!!!!

Average - The "mean" is the average of a set of data.  Sounds impressive?  Well there can be problems here too.  What if someone is arguing that the employees at a particular organization are so well paid, that they do not need a raise - and they demonstrate that the AVERAGE salary is - say - $50,000?   The first thing you should do is look at what they are AVERAGING.  What is the RANGE of their data??  For example, if the highest paid person is making $60,000, and the lowest paid person is making $40,000 - the average might be reasonable.  BUT what if you discover that the data has the characteristics of wide dispersal???? That you find that only 2 people make over $50,000  - in fact they are making $125,000 !!!!!  while no one else is even making $30,000 !!!!!  The point is, you need to examine the data being averaged - and look at the range of the data.

Median - This is the point in the data where 1/2 the data is above, and the other 1/2 is below. 
(this is the statistical measure often used by the US government, especially when presenting data on income of US families.  The reason is - that when you have data which is "dispersed" - like the differences in income - the median is a more "reliable" measure than the "average").

Mode - The most frequent response in a set of data.

Example:   Salaries at a fictional organization

MODE:                      $30,000
MEAN (average)      $44,600
MEDIAN:                   $40,000 

IF you are arguing IN FAVOR of  a raise for these employees - what statistical measure would you use??? 

IF you are arguing AGAINST a raise for these employees - what statistical measure would you use ???